Embedding data points problem

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Desiree 2020-4-6

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https://ww2.mathworks.cn/matlabcentral/answers/515684-embedding-data-points-problem

编辑： Desiree 2020-4-6

Hello. I wrote this following which I have theta data column points (1024 in my case)and finds the eigenvectors of the Laplace-Beltrami operator using density invariant normalization.

theta=0:2*pi/1023:2*pi;
t=-1.5:3/511:1.5;
P=my_data(theta,t);
B=(1/size(P,2))*sum(P,2);
U=zeros(size(P));
for l=1:size(P,2)
    U(:,l)=B;
end
X=P-U;
epsilon=0.01
W=zeros(size(P,2),size(P,2));
T=zeros(size(P,2),size(P,2));
for i=1:size(P,2)
    for j=1:size(P,2)
        W(i,j)=exp(-norm(X(:,i)-P(:,j))/(sqrt(2*epsilon)));
    end
end
a=(sum(W,2))';
D=zeros(size(W,1),size(W,2));
for k=1:size(W,2)
    D(k,k)=a(k);
end
T=inv(D)*W*inv(D);
b=(sum(T,2))';
D2=zeros(size(W,1),size(W,2));
for m=1:size(W,2)
    D2(m,m)=b(m);
end
Anorm=inv(D2)*T;
G=(D2^(-0.5))*T*(D2^(-0.5));
[V,gamma]=eig(G);

Now I need to make embedding of each column of X onto the first 3 and 4 non trivial eigenvectors excluding V(:,1) but I don’t know how to do it. Help is greatly appreciated!